Ready for outside

I have 20 chicks there are two weeks old and making a mess in the house and noisy! they have grown nice looking feathers, at what age and point should they be transferred outside? I am in Fallon, Nevada and the current temps range from 44 deg in the day to 20's at night and may drop down to the 10's in the mountains here.
I think the overnight temps might be to cold even with an heating lamp in the coop which is 8x8 but I need some help with this as this is my first batch of chickens and new to it all.
If I can't move them out permanent could I put them out there in the day when the temp is in the 40's and sun is out and bring them in house at night or would they survive an all nighter?

I would certainly try them out there during the day, at least. Just monitor the situation. They will be OK unless they pile on top of each other, smothering the ones at the bottom. You probably won't be able to maintain recommended brooder temps, but that doesn't mean they won't survive it and do just fine. Mine have been out and about all day since they were a week old. Their mama keeps them warm at night, but they stopped going under her during the day pretty early. We're not as cold as you, quite, although we were having a cold snap that week and our temps were in the teens and 20's at night.

If the sun is out, they may be ok during the day, but they are not fully feathered until they are 8 weeks. And they should not be outside this time of year before they are fully feathered. If there is wind during the day, I would say no, but if it is sunny and calm, then they will have a blast.

You really shouldn't put them outside until they are at least 2 months old, so they are fully feathered and protected from cocci. Before then, you're just asking for losses, really. Your chicks are nowhere near ready for 40 degree weather.

If you need to, expand the brooder. If you can set one up in your coop, where they are still under infrared heat lamps, out of the wind, etc. then that's probably okay but you need to check the temps.

My hatchery variety Delawares have been in their outside (heated) brooder since the day I received them (three days old). They have had free access to the outside elements since two weeks old (during the day). It got below freezing when they were less than three weeks old. They play outside in the high winds, rain and even hail, lol.

ETA: Your number of chicks is great for creation of mass body heat. Get yourself at least TWO heat lamps for the coop. Hang them double-secured from the ceiling/etc and adjust so that a couple inches off the ground is the ideal temp. Chain-link works great for hanging the lamps (with a separate rope/cord tied off to keep the lamp from falling all the way to the floor and causing a fire). Set this up and wait a day or two or three, before bothering with an "accurate" temperature reading via a thermometer.